Finite Group Databasebeta

← C2×#11741055 #14232385

Subgroups — C2×#11741055 #14232385

Order 1792.

1962 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#553C211yesmaximal, characteristic, complemented
2C2×#90254C211yesmaximal, characteristic, complemented
3#11741055C2116yesmaximal, direct product factor
4C2×#89838C211yesmaximal, characteristic, complemented
5C2×#89837C211yesmaximal, characteristic, complemented
6C2×#89811C211yesmaximal, characteristic, complemented
7C2×#89810C211yesmaximal, characteristic, complemented
8C2×#89807C211yesmaximal, characteristic, complemented
9C2×#89807C211yesmaximal, characteristic, complemented
10C2×#89783C211yesmaximal, characteristic, complemented
11C2×#89779C211yesmaximal, characteristic, complemented
12C2×#89786C211yesmaximal, characteristic, complemented
13C2×#89775C211yesmaximal, characteristic, complemented
14C2×#89770C211yesmaximal, characteristic, complemented
15C2×#89739C211yesmaximal, characteristic, complemented
16C2×#89736C211yesmaximal, characteristic, complemented
17C7×#553—24no—
18C7×#553C2218yescomplemented
19C2×C7×#126—21no—
20C2×C7×#125C2211yescharacteristic
21C2×C7×#123—21no—
22C2×C7×#121—21no—
23C2×C7×#121C2211yescharacteristic
24C2×C7×#121C2211yescharacteristic
25C2×C4×C7×D4—21no—
26C2×C4×C7×D4C2211yescharacteristic
27C2×C4×C7×D4C2211yescharacteristic
28C2×C7×#117C2211yescharacteristic
29C22×C7×C4⋊C4C2211yescharacteristic
30C2×#6501—21no—
31C22×#1141C2211yescharacteristic
32C2×#6493C2211yescharacteristic
33C2×#6493C2211yescharacteristic
34C2×#6489C2211yescharacteristic
35C2×#6489C2211yescharacteristic
36C22×#1136C2211yescharacteristic
37C23×C7⋊C8C2211yescharacteristic
38#90254—24no—
39#90254C2218yescomplemented
40C2×#6455—21no—
41C2×#6448—21no—
42C2×#6448—21no—
43C2×C4×D28C2211yescharacteristic
44C2×#6432C2211yescharacteristic
45C2×#6406C2211yescharacteristic
46C2×#6406C2211yescharacteristic
47C2×#6406C2211yescharacteristic
48C2×C22⋊(C7⋊C8)C2211yescharacteristic
49C2×C22⋊(C7⋊C8)C2211yescharacteristic
50#89838C2218yescomplemented
51#89837C2218yescomplemented
52#89811C2218yescomplemented
53#89810C2218yescomplemented
54#89807C2218yescomplemented
55#89807C2218yescomplemented
56#89786C2218yescomplemented
57#89783C2218yescomplemented
58#89779C2218yescomplemented
59#89775C2218yescomplemented
60#89770C2218yescomplemented
61#89739C2218yescomplemented
62C2×#6383C2211yescharacteristic
63C2×#6383C2211yescharacteristic
64C2×#6383C2211yescharacteristic
65#89736C2218yescomplemented
66C2×#6382C2211yescharacteristic
67C2×#6382C2211yescharacteristic
68C2×#6382C2211yescharacteristic
69C2×#6382C2211yescharacteristic
70C2×#6381C2211yescharacteristic
71C2×#6381C2211yescharacteristic
72C2×#6381C2211yescharacteristic
73C2×#6381C2211yescharacteristic
74C2×#6381C2211yescharacteristic
75C2×C4⋊(C7⋊C8)C2211yescharacteristic
76C2×#6377C2211yescharacteristic
77C2×#3347—71nomaximal, Sylow
78C22×C7×D4—21no—
79C22×C7×D4—21no—
80C22×C7×D4D411yescharacteristic
81C22×C7×D4C2311yescharacteristic
82C23×C4×C7—21no—
83C23×C4×C7—21no—
84C23×C4×C7C2311yescharacteristic
85C23×C4×C7C2311yescharacteristic
86C22×C22⋊D7—21no—
87C22×C22⋊D7—21no—
88C22×D28C2311yescharacteristic
89C22×C4×D7—21no—
90C22×Dic14—21no—
91C7×#126—28no—
92C7×#125—22no—
93C7×#125C2314yes—
94C7×#123—28no—
95C7×#121—28no—
96C7×#121—22no—
97C7×#121—22no—
98C7×#121C2314yes—
99C7×#121C2314yes—
100C4×C7×D4—28no—
101C4×C7×D4—22no—
102C4×C7×D4D414yes—
103C4×C7×D4C2314yes—
104C4×C7×D4C2314yes—
105C7×#117—22no—
106C7×#117C2314yes—
107C2×C7×C4⋊C4—21no—
108C2×C7×C4⋊C4—22no—
109C2×C7×C4⋊C4—21no—
110C2×C7×C4⋊C4—21no—
111C2×C7×C4⋊C4D411yescharacteristic
112C2×C7×C4⋊C4C2311yescharacteristic
113C2×C7×C4⋊C4C2311yescharacteristic
114C2×C7×C4⋊C4C2311yescharacteristic
115C2×C7×C4⋊C4C2314yes—
116C2×C7×C22⋊C4—21no—
117C2×C7×C22⋊C4—21no—
118C2×C7×C22⋊C4—21no—
119C2×C7×C22⋊C4—21no—
120C2×C7×C22⋊C4D411yescharacteristic
121C2×C7×C22⋊C4D411yescharacteristic
122C2×C42×C7—21no—
123C2×C42×C7C2311yescharacteristic
124C2×C22⋊Dic7—21no—
125C2×C22⋊Dic7—21no—
126#6501—28no—
127C2×#1141—24no—
128C2×#1141C2314yes—
129#6493—22no—
130#6493—22no—
131#6493C2314yes—
132#6493C2314yes—
133C2×(C2×D7)⋊C4—21no—
134C2×(C2×D7)⋊C4—21no—
135C2×(C2×D7)⋊C4—21no—
136#6489—22no—
137#6489—22no—
138#6489C2314yes—
139#6489C2314yes—
140C2×C4⋊Dic7—21no—
141C2×C4⋊Dic7C2311yescharacteristic
142C2×C4⋊Dic7C2311yescharacteristic
143C2×C4⋊Dic7C2311yescharacteristic
144C2×C4×Dic7—21no—
145C2×C4×Dic7—21no—
146C2×#1136—24no—
147C2×#1136C2314yes—
148C22×C7⋊C8—24no—
149C22×C7⋊C8C2311yescharacteristic
150C22×C7⋊C8C2311yescharacteristic
151C22×C7⋊C8C2311yescharacteristic
152C22×C7⋊C8C2314yes—
153C22×C7⋊C8C2311yescharacteristic
154#6455—28no—
155#6448—28no—
156#6448—28no—
157C4×D28—22no—
158C4×D28C2314yes—
159#6432—22no—
160#6432C2314yes—
161#6406C2314yes—
162#6406C2314yes—
163#6406C2314yes—
164C22⋊(C7⋊C8)C2314yes—
165C22⋊(C7⋊C8)C2314yes—
166#6383C2314yes—
167#6383C2314yes—
168#6383C2314yes—
169#6382C2314yes—
170#6382C2314yes—
171#6382C2314yes—
172#6382C2314yes—
173#6381C2314yes—
174#6381C2314yes—
175#6381C2314yes—
176#6381C2314yes—
177#6381C2314yes—
178C4⋊(C7⋊C8)C2314yes—
179#6377C2314yes—
180C2×#555—71no—
181C2×#553D711yescharacteristic, complemented
182#3347—716no—
183C2×#501—71no—
184C2×#482—71no—
185C2×#482—71no—
186C2×#482—71no—
187C2×#480—71no—
188C2×#478—71no—
189C2×#474—71no—
190C2×#469—71no—
191C2×#466—71no—
192C2×#442—71no—
193C2×#435—71no—
194C2×#428—71no—
195C2×#427—71no—
196C24×C7—21no—
197C24×C7C2×D411yescharacteristic
198C24×C7C2×D411yescharacteristic
199C23×D7—21no—
200C2×C7×D4—24no—
201C2×C7×D4—24no—
202C2×C7×D4—21no—
203C2×C7×D4—22no—
204C2×C7×D4—22no—
205C2×C7×D4—42no—
206C2×C7×D4—44no—
207C2×C7×D4—82no—
208C2×C7×D4C2×D414yes—
209C2×C7×D4C2412yes—
210C22×C4×C7—22no—
211C22×C4×C7—22no—
212C22×C4×C7—22no—
213C22×C4×C7—22no—
214C22×C4×C7—21no—
215C22×C4×C7—21no—
216C22×C4×C7—21no—
217C22×C4×C7—24no—
218C22×C4×C7—24no—
219C22×C4×C7—82no—
220C22×C4×C7—82no—
221C22×C4×C7C2×D411yescharacteristic
222C22×C4×C7C2×D411yescharacteristic
223C22×C4×C7C2×D411yescharacteristic
224C22×C4×C7C2×D412yes—
225C22×C4×C7C2×D412yes—
226C22×C4×C7C2×D411yescharacteristic
227C22×C4×C7C2412yes—
228C22×C4×C7C2412yes—
229C22×C4×C7C2411yescharacteristic
230C2×C22⋊D7—24no—
231C2×C22⋊D7—24no—
232C2×C22⋊D7—82no—
233C2×C22⋊D7—82no—
234C22×Dic7—21no—
235C22×Dic7—21no—
236C22×Dic7—21no—
237C2×D28—22no—
238C2×D28—22no—
239C2×D28—21no—
240C2×D28C2412yes—
241C2×C4×D7—24no—
242C2×C4×D7—44no—
243C2×Dic14—24no—
244C2×Dic14—82no—
245C7×C4⋊C4—21no—
246C7×C4⋊C4—21no—
247C7×C4⋊C4—24no—
248C7×C4⋊C4—24no—
249C7×C4⋊C4—24no—
250C7×C4⋊C4—21no—
251C7×C4⋊C4C2×D414yes—
252C7×C4⋊C4C2412yes—
253C7×C4⋊C4C2412yes—
254C7×C4⋊C4C2412yes—
255C7×C22⋊C4—24no—
256C7×C22⋊C4—24no—
257C7×C22⋊C4—24no—
258C7×C22⋊C4—24no—
259C7×C22⋊C4C2×D414yes—
260C7×C22⋊C4C2×D414yes—
261C42×C7—24no—
262C42×C7C2×D412yes—
263C42×C7C2412yes—
264C22⋊Dic7—24no—
265C22⋊Dic7—24no—
266#1141—28no—
267(C2×D7)⋊C4—24no—
268(C2×D7)⋊C4—24no—
269(C2×D7)⋊C4—24no—
270C4⋊Dic7—21no—
271C4⋊Dic7—21no—
272C4⋊Dic7—24no—
273C4⋊Dic7—21no—
274C4⋊Dic7C2412yes—
275C4⋊Dic7C2412yes—
276C4⋊Dic7C2412yes—
277C4×Dic7—24no—
278C4×Dic7—24no—
279#1136—28no—
280C2×C7⋊C8—22no—
281C2×C7⋊C8—22no—
282C2×C7⋊C8—22no—
283C2×C7⋊C8—28no—
284C2×C7⋊C8#4114yes—
285C2×C7⋊C8C2412yes—
286C2×C7⋊C8C2412yes—
287C2×C7⋊C8C2412yes—
288C2×C7⋊C8C2412yes—
289C22×D8—71no—
290C22×M16—71no—
291C23×C8—71no—
292#555—78no—
293#555—144no—
294#553—24no—
295#553C2×D718yescomplemented
296C2×C4⋊Q8—71no—
297C2×#126—21no—
298C2×#125C2×D711yescharacteristic
299C2×#124—141no—
300C2×#124—141no—
301C2×#123—21no—
302C2×#121—21no—
303C2×#121—71no—
304C2×#121—71no—
305C2×#121—141no—
306C2×#121C2×D711yescharacteristic
307C2×#121C2×D711yescharacteristic
308C2×C4×D4—21no—
309C2×C4×D4—71no—
310C2×C4×D4C2×D711yescharacteristic
311C2×C4×D4C2×D711yescharacteristic
312C2×#117—71no—
313C2×#117—71no—
314C2×#117—141no—
315C2×#117C2×D711yescharacteristic
316C22×C4⋊C4C2×D711yescharacteristic
317#501—78no—
318#482—78no—
319#482—78no—
320#482—78no—
321#480—78no—
322#478—78no—
323#474—78no—
324#469—78no—
325#466—78no—
326#442—78no—
327#435—78no—
328#428—78no—
329#427—78no—
330C2×#107—71no—
331C2×#107—71no—
332C2×#107—71no—
333C2×#107—71no—
334C2×#107—71no—
335C2×#106—71no—
336C2×#106—71no—
337C2×#106—71no—
338C2×#106—71no—
339C2×C4⋊C8—71no—
340C2×#102—71no—
341C2×#102—71no—
342C2×#102—71no—
343C2×#102—71no—
344C2×#102—71no—
345C2×#102—71no—
346C2×C22⋊C8—71no—
347C2×C22⋊C8—71no—
348C2×#97—71no—
349C23×C7—22no—
350C23×C7—22no—
351C23×C7—22no—
352C23×C7—22no—
353C23×C7—22no—
354C23×C7—22no—
355C23×C7—22no—
356C23×C7—42no—
357C23×C7—42no—
358C23×C7—42no—
359C23×C7C22×D412yes—
360C23×C7C22×D412yes—
361C23×C7C22×D411yescharacteristic
362C22×D7—22no—
363C22×D7—42no—
364C22×D7—42no—
365C22×D7—42no—
366C7×D4—22no—
367C7×D4—22no—
368C7×D4—44no—
369C7×D4—48no—
370C7×D4—42no—
371C7×D4—84no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—24no—
377C2×C4×C7—24no—
378C2×C4×C7—22no—
379C2×C4×C7—22no—
380C2×C4×C7—22no—
381C2×C4×C7—22no—
382C2×C4×C7—22no—
383C2×C4×C7—22no—
384C2×C4×C7—22no—
385C2×C4×C7—42no—
386C2×C4×C7—42no—
387C2×C4×C7—42no—
388C2×C4×C7—84no—
389C2×C4×C7—84no—
390C2×C4×C7C22×D412yes—
391C2×C4×C7C22×D412yes—
392C2×C4×C7C22×D412yes—
393C2×C4×C7C22×D412yes—
394C2×C4×C7C22×D411yescharacteristic
395C2×C4×C7C2×#4112yes—
396C2×C4×C72−1+412yes—
397C2×C4×C7C2511yescharacteristic
398C22⋊D7—84no—
399C22⋊D7—84no—
400C2×Dic7—22no—
401C2×Dic7—22no—
402C2×Dic7—22no—
403C2×Dic7—42no—
404C2×Dic7—42no—
405C2×Dic7—42no—
406D28—22no—
407D28—22no—
408D28—42no—
409C4×D7—48no—
410Dic14—84no—
411C7⋊C8—22no—
412C7⋊C8—22no—
413C7⋊C8—22no—
414C7⋊C8C2×#4114yes—
415C22×Q8—141no—
416C22×D4—21no—
417C22×D4—21no—
418C22×D4—71no—
419C22×D4—141no—
420C22×D4—141no—
421C22×D4C22⋊D711yescharacteristic
422C22×D4C22×D711yescharacteristic
423C23×C4—21no—
424C23×C4—21no—
425C23×C4—141no—
426C23×C4C22×D711yescharacteristic
427C23×C4C22×D711yescharacteristic
428C2×D8—74no—
429C2×D8—144no—
430C2×M16—74no—
431C2×M16—144no—
432C22×C8—71no—
433C22×C8—71no—
434C22×C8—74no—
435C22×C8—71no—
436C22×C8—71no—
437C22×C8—144no—
438C4⋊Q8—74no—
439C4⋊Q8—142no—
440#126—28no—
441#125—22no—
442#125C22×D714yes—
443#124—148no—
444#124—148no—
445#123—28no—
446#121—28no—
447#121—22no—
448#121—22no—
449#121—74no—
450#121—74no—
451#121—148no—
452#121—142no—
453#121—142no—
454#121C22×D714yes—
455#121C22×D714yes—
456C4×D4—28no—
457C4×D4—22no—
458C4×D4—74no—
459C4×D4—142no—
460C4×D4C22⋊D714yes—
461C4×D4C22×D714yes—
462C4×D4C22×D714yes—
463#117—22no—
464#117—74no—
465#117—74no—
466#117—142no—
467#117—142no—
468#117—148no—
469#117C22×D714yes—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—71no—
475C2×C4⋊C4—71no—
476C2×C4⋊C4—71no—
477C2×C4⋊C4—141no—
478C2×C4⋊C4C22⋊D711yescharacteristic
479C2×C4⋊C4C22×D711yescharacteristic
480C2×C4⋊C4C22×D711yescharacteristic
481C2×C4⋊C4C22×D714yes—
482C2×C4⋊C4C22×D711yescharacteristic
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—141no—
488C2×C22⋊C4—141no—
489C2×C22⋊C4—141no—
490C2×C22⋊C4—141no—
491C2×C22⋊C4—141no—
492C2×C22⋊C4C22⋊D711yescharacteristic
493C2×C22⋊C4C22⋊D711yescharacteristic
494C2×C42—21no—
495C2×C42—141no—
496C2×C42—141no—
497C2×C42C22×D711yescharacteristic
498#107—74no—
499#107—74no—
500#107—74no—
501#107—74no—
502#107—74no—
503#106—74no—
504#106—74no—
505#106—74no—
506#106—74no—
507C4⋊C8—74no—
508#102—74no—
509#102—74no—
510#102—74no—
511#102—74no—
512#102—74no—
513#102—74no—
514C22⋊C8—74no—
515C22⋊C8—74no—
516#97—74no—
517C22×C7—22no—
518C22×C7—22no—
519C22×C7—22no—
520C22×C7—22no—
521C22×C7—22no—
522C22×C7—22no—
523C22×C7—44no—
524C22×C7—44no—
525C22×C7—42no—
526C22×C7—42no—
527C22×C7—42no—
528C22×C7—84no—
529C22×C7#54712yes—
530C22×C7#57512yes—
531C22×C7#57612yes—
532C22×C7C23×D411yescharacteristic
533C2×D7—42no—
534C2×D7—42no—
535C2×D7—42no—
536C2×D7—84no—
537C4×C7—22no—
538C4×C7—22no—
539C4×C7—22no—
540C4×C7—22no—
541C4×C7—42no—
542C4×C7—42no—
543C4×C7—42no—
544C4×C7#54712yes—
545C4×C7C22×#4111yescharacteristic
546C4×C7C2×2−1+411yescharacteristic
547Dic7—42no—
548Dic7—42no—
549Dic7—42no—
550C24—21no—
551C24—141no—
552C24C2×C22⋊D711yescharacteristic
553C24C2×C22⋊D711yescharacteristic
554C2×Q8—144no—
555C2×Q8—562no—
556C2×D4—24no—
557C2×D4—24no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—21no—
561C2×D4—42no—
562C2×D4—44no—
563C2×D4—72no—
564C2×D4—82no—
565C2×D4—144no—
566C2×D4—144no—
567C2×D4—142no—
568C2×D4—142no—
569C2×D4—141no—
570C2×D4—562no—
571C2×D4—562no—
572C2×D4C2×C22⋊D714yes—
573C2×D4C23×D712yes—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—24no—
582C22×C4—24no—
583C22×C4—82no—
584C22×C4—82no—
585C22×C4—141no—
586C22×C4—141no—
587C22×C4—141no—
588C22×C4—144no—
589C22×C4—284no—
590C22×C4C2×C22⋊D712yes—
591C22×C4C2×C22⋊D712yes—
592C22×C4C2×C22⋊D711yescharacteristic
593C22×C4C2×C22⋊D711yescharacteristic
594C22×C4C2×C22⋊D711yescharacteristic
595C22×C4C2×C22⋊D711yescharacteristic
596C22×C4C23×D712yes—
597C22×C4C23×D712yes—
598C22×C4C23×D711yescharacteristic
599D8—148no—
600M16—148no—
601C2×C8—74no—
602C2×C8—72no—
603C2×C8—72no—
604C2×C8—72no—
605C2×C8—72no—
606C2×C8—148no—
607C2×C8—142no—
608C2×C8—142no—
609C2×C8—142no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—24no—
615C4⋊C4—21no—
616C4⋊C4—72no—
617C4⋊C4—72no—
618C4⋊C4—72no—
619C4⋊C4—141no—
620C4⋊C4—141no—
621C4⋊C4—141no—
622C4⋊C4—144no—
623C4⋊C4C2×C22⋊D714yes—
624C4⋊C4C23×D712yes—
625C4⋊C4C23×D712yes—
626C4⋊C4C23×D712yes—
627C22⋊C4—24no—
628C22⋊C4—24no—
629C22⋊C4—24no—
630C22⋊C4—24no—
631C22⋊C4—144no—
632C22⋊C4—144no—
633C22⋊C4—144no—
634C22⋊C4—144no—
635C22⋊C4—144no—
636C22⋊C4C2×C22⋊D714yes—
637C22⋊C4C2×C22⋊D714yes—
638C42—24no—
639C42—144no—
640C42—144no—
641C42C2×C22⋊D712yes—
642C42C23×D712yes—
643C2×C7—42no—
644C2×C7—42no—
645C2×C7—82no—
646C2×C7#334714yescomplemented
647C2×C7C2×#54711yescharacteristic
648C2×C7C2×#57511yescharacteristic
649C2×C7C2×#57611yescharacteristic
650D7—82no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—142no—
662C23—282no—
663C23—282no—
664C23—282no—
665C23C22×C22⋊D712yes—
666C23C22×C22⋊D712yes—
667C23C22×C22⋊D711yescharacteristic
668Q8—564no—
669D4—22no—
670D4—22no—
671D4—44no—
672D4—48no—
673D4—42no—
674D4—84no—
675D4—142no—
676D4—142no—
677D4—282no—
678D4—564no—
679D4—564no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—84no—
697C2×C4—84no—
698C2×C4—142no—
699C2×C4—142no—
700C2×C4—142no—
701C2×C4—288no—
702C2×C4—282no—
703C2×C4—282no—
704C2×C4—282no—
705C2×C4D7×#4112yes—
706C2×C4#655412yes—
707C2×C4C22×C22⋊D712yes—
708C2×C4C22×C22⋊D712yes—
709C2×C4C22×C22⋊D712yes—
710C2×C4C22×C22⋊D712yes—
711C2×C4C22×C22⋊D711yescharacteristic
712C2×C4C24×D711yescharacteristic
713C8—74no—
714C8—142no—
715C8—142no—
716C8—142no—
717C7C2×#334711yescharacteristic, complemented, Sylow
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—44no—
725C22—44no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—84no—
730C22—282no—
731C22—282no—
732C22—282no—
733C22—564no—
734C22#9051312yes—
735C22#9051512yes—
736C22#9052612yes—
737C22C23×C22⋊D711yescharacteristic
738C4—22no—
739C4—22no—
740C4—22no—
741C4—22no—
742C4—42no—
743C4—42no—
744C4—42no—
745C4—282no—
746C4—282no—
747C4—282no—
748C4#9051512yes—
749C4C2×D7×#4111yescharacteristic
750C4C2×#655411yescharacteristic
751C2—42no—
752C2—42no—
753C2—82no—
754C2—562no—
755C2#1174105514yesdirect product factor
756C2C2×#9051311yescharacteristic
757C2C2×#9051511yescharacteristic
758C2C2×#9052611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#553C2
socleC23×C7C22×D4
hypercenterC2×#553D7
hypocenterC7C2×#3347
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C7×#553C2semidirect
2. C2×#90254C2semidirect
3. #11741055C2direct (N × H)
4. C2×#89838C2semidirect
5. C2×#89837C2semidirect
6. C2×#89811C2semidirect
7. C2×#89810C2semidirect
8. C2×#89807C2semidirect
9. C2×#89807C2semidirect
10. C2×#89783C2semidirect
11. C2×#89779C2semidirect
12. C2×#89786C2semidirect
13. C2×#89775C2semidirect
14. C2×#89770C2semidirect
15. C2×#89739C2semidirect
16. C2×#89736C2semidirect
18. C7×#553C22semidirect
39. #90254C22semidirect
50. #89838C22semidirect
51. #89837C22semidirect
52. #89811C22semidirect
53. #89810C22semidirect
54. #89807C22semidirect
55. #89807C22semidirect
56. #89786C22semidirect
57. #89783C22semidirect
58. #89779C22semidirect
59. #89775C22semidirect
60. #89770C22semidirect
61. #89739C22semidirect
65. #89736C22semidirect
181. C2×#553D7semidirect
295. #553C2×D7semidirect
646. C2×C7#3347semidirect
717. C7C2×#3347semidirect
755. C2#11741055direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C7×#5532
C2×#902542
#117410552
C2×#898382
C2×#898372
C2×#898112
C2×#898102
C2×#898072
C2×#897832
C2×#897792
C2×#897862
C2×#897752
C2×#897702
C2×#897392
C2×#897362
C2×#33477